An Alternative Analysis of the Plane Stick-Slip Problem

Abstract

The plane stick-slip problem has been solved analytically using the separation of variable technique. The essence of the mathematical procedure is to solve the problem separately for the “stick” and the “slip” regions and then to match the two solutions at the exit plane. The present solution, which is relatively easy to evaluate, yields results that compare favorably with those obtained by the Wiener-Hopf technique. Furthermore, the stick-slip solution has been used to estimate the expansion of a two-dimensional plane Newtonian jet at very low Reynolds numbers. For capillary numbers less than 0.1, the approximate method predicts swell ratios that are in fairly good agreement with those obtained from a more elaborate numerical solution of the jet swell problem.